Digital Interface to Analog Circuits is an example of Mixed Signal Design. Generating Digital Control Signals from the Analog sections in instruments is also done by Mixed Signal Circuit.
A/D Convertors and D/A Convertors are like Mixed Signal Chips. A Digital Potentiometer that controls an analog signal amplitude with a digital byte or word, figures in Mixed Design Circuit.
Operational Amplifiers - With a few Op-Amps and a regulated Power supply, many Instrumentation and Process control equipment can be designed. The Human Brain understands Numbers, Quantity and it regulation very well ! On the right you can see a analog controller based on opamps and discrete devices. A Heater, Fan and Motor is regulated, controlled and timed for a process.
Analog is about numbers, the circuits can be understood and designed mathematically or empirically. Designing and Building a True RMS Rectifier with Op-Amps, will help a designer digest many Op-Amp capabilities.
The very first designs that came about were analog designs, a Vacuum Tube amplifier is an example. Analog is the representation of data or physical parameter in an accurate and precise decimal number like + 72.182 mV. The greater the resolution required, the more demanding is the design for achieving high accuracy and low drift. Digital circuits have only two voltage levels, high and low, the third state of floating, Hi-Z or high impedance is only for multiplexing or sharing a bus. This is done so that devices dont drive into each other and it is also used in external port drivers.
Analog Design and Circuits
As an analogy, see the conventional water tap as an analog control, an electric light ON-OFF switch as a digital control.
Analog Circuits Instrumentation
Most of the sensor interface and instrument inputs are analog; even if it event based like a limit switch, analog circuit protection and signal conditioning is required before it reaches the level sensitive digital circuit blocks.
Starting with Schmitt triggers and to the VCO and A-D Converters, are grades of Mixed Circuits. I feel Comparators like LM339, Timers like the 555 and Phase Locked Loop PLL are fundamental mixed circuits as they have a analog voltage detection.
DSP and uC with built in A-D or D-A or even SOC are Public ASICs and Fall in the Embedded Systems Block. Public ASICs are not user specific, they can be branded, numbered and provided with Application notes for the use of the Design Departments of any firm. User Specific ASICs are custom built and have only an application with that manufacturer for a Specific Product type. This also protects the IP of Code and Device Design.